Then you have your answer: Support is non-boolean. I don’t think a boolean concept of consistency of observations with anything makes sense, though (consistent would mean P(E|H)>0, but observations never have a probability of 0 anyway, so every observation would be consistent with everything, or you’d need an arbitrary cut-off. P(observe black sheep|all sheep are white) > 0, but is very small ).
Some theories predict that some things won’t happen (0 probability). I consider this kind of theory important.
You say I have my answer, but you have not answered. I don’t think you’ve understood the problem. To try to repeat myself less, check out the discussion here, currently at the bottom:
Some theories predict that some things won’t happen (0 probability). I consider this kind of theory important.
But they don’t predict that you won’t hallucinate, or misread the experimental data, or whatever. Some things not happening doesn’t mean some things won’t be observed.
You say I have my answer, but you have not answered.
You asked how support differed form consistent. Boolean vs real number is a difference. Even if you arbitrarily decide that real numbers are not allowed and only booleans are that doesn’t mean that differentiating between their use of real numbers and your use of booleans is inconsistent on part of those who use real numbers.
Support is the same thing as more consistent with that hypothesis than with the alternatives (P(E|H) >P(E|~H)).
What is “more consistent”?
Consistent = does not contradict. But you can’t not-contradict more. It’s a boolean issue.
Then you have your answer: Support is non-boolean. I don’t think a boolean concept of consistency of observations with anything makes sense, though (consistent would mean P(E|H)>0, but observations never have a probability of 0 anyway, so every observation would be consistent with everything, or you’d need an arbitrary cut-off. P(observe black sheep|all sheep are white) > 0, but is very small ).
Some theories predict that some things won’t happen (0 probability). I consider this kind of theory important.
You say I have my answer, but you have not answered. I don’t think you’ve understood the problem. To try to repeat myself less, check out the discussion here, currently at the bottom:
http://lesswrong.com/lw/54u/bayesian_epistemology_vs_popper/3urr?context=3
But they don’t predict that you won’t hallucinate, or misread the experimental data, or whatever. Some things not happening doesn’t mean some things won’t be observed.
You asked how support differed form consistent. Boolean vs real number is a difference. Even if you arbitrarily decide that real numbers are not allowed and only booleans are that doesn’t mean that differentiating between their use of real numbers and your use of booleans is inconsistent on part of those who use real numbers.